Research Article
New One-Sided EWMA t Charts without and with Variable Sampling Intervals for Monitoring the Process Mean
Table 5
The (ARL, MRL, SDRL) profiles of three different upper-sided run rules t charts when ARL0 = 200 and n ∈ {5, 7, 9, 11}.
| n | Chart | λ | UCL+ | δ | 0.1 | 0.3 | 0.5 | 0.7 | 1.0 | 1.5 | 2 | 3 |
| 5 | RR2,3-t | — | 2.0762 | (200.00 | 139 | 198.14) | (100.18 | 70 | 98.38) | (31.54 | 22 | 29.85) | (13.10 | 10 | 11.51) | (6.88 | 5 | 5.36) | (3.68 | 3 | 2.17) | (2.31 | 2 | 0.66) | (2.05 | 2 | 0.00) | (2.00 | 2 | 0.01) | RR3,4-t | — | 1.2980 | (200.00 | 139 | 197.17) | (87.36 | 61 | 84.64) | (24.10 | 17 | 21.59) | (10.12 | 8 | 7.76) | (5.84 | 4 | 3.50) | (3.79 | 3 | 1.32) | (3.08 | 3 | 0.31) | (3.01 | 3 | 0.07) | (3.00 | 3 | 0.00) | RR4,5-t | — | 0.8755 | (200.00 | 140 | 196.29) | (80.80 | 57 | 77.26) | (21.39 | 16 | 18.15) | (9.49 | 7 | 6.37) | (6.01 | 5 | 2.82) | (4.47 | 4 | 0.98) | (4.03 | 4 | 0.19) | (4.00 | 4 | 0.03) | (4.00 | 4 | 0.00) | U-NEWMA | 0.1 | 0.6811 | (200.45 | 140 | 198.20) | (56.71 | 41 | 51.02) | (14.41 | 12 | 9.35) | (7.45 | 7 | 3.69) | (5.04 | 5 | 2.11) | (3.46 | 3 | 1.26) | (2.38 | 2 | 0.78) | (1.90 | 2 | 0.60) | (1.43 | 1 | 0.50) | U-NEWMA | 0.2 | 1.1493 | (201.26 | 141 | 198.92) | (74.34 | 53 | 70.89) | (17.96 | 14 | 14.27) | (8.09 | 7 | 5.04) | (5.02 | 5 | 2.56) | (3.26 | 3 | 1.37) | (2.17 | 2 | 0.78) | (1.71 | 2 | 0.58) | (1.27 | 1 | 0.44) | U-NEWMA | 0.3 | 1.5763 | (199.58 | 139 | 198.32) | (87.67 | 61 | 85.70) | (23.31 | 17 | 20.65) | (9.66 | 8 | 7.16) | (5.52 | 5 | 3.37) | (3.33 | 3 | 1.61) | (2.10 | 2 | 0.82) | (1.63 | 2 | 0.59) | (1.19 | 1 | 0.39) | U-NEWMA | 0.5 | 2.4137 | (198.78 | 138 | 198.32) | (107.58 | 75 | 106.77) | (35.70 | 25 | 34.22) | (14.96 | 11 | 13.43) | (7.71 | 6 | 6.19) | (3.94 | 3 | 2.55) | (2.17 | 2 | 1.05) | (1.57 | 1 | 0.64) | (1.13 | 1 | 0.34) | U-NEWMA | 1 | 4.5961 | (198.50 | 138 | 197.91) | (129.07 | 90 | 128.30) | (58.35 | 40 | 58.02) | (29.23 | 20 | 28.74) | (16.17 | 11 | 15.73) | (7.75 | 6 | 7.23) | (3.19 | 2 | 2.64) | (1.82 | 1 | 1.22) | (1.12 | 1 | 0.36) | 7 | RR2,3-t | — | 1.8979 | (200.00 | 139 | 198.14) | (85.39 | 60 | 83.60) | (21.92 | 16 | 20.27) | (8.45 | 6 | 6.91) | (4.50 | 3 | 3.00) | (2.68 | 2 | 1.11) | (2.06 | 2 | 0.26) | (2.00 | 2 | 0.05) | (2.00 | 2 | 0.00) | RR3,4-t | — | 1.2319 | (200.00 | 139 | 197.17) | (74.29 | 52 | 71.60) | (17.42 | 13 | 14.98) | (7.24 | 6 | 4.91) | (4.47 | 4 | 2.08) | (3.30 | 3 | 0.69) | (3.01 | 3 | 0.12) | (3.00 | 3 | 0.01) | (3.00 | 3 | 0.00) | RR4,5-t | — | 0.8446 | (200.00 | 140 | 196.29) | (68.81 | 49 | 65.31) | (15.99 | 12 | 12.81) | (7.28 | 5 | 4.15) | (5.02 | 4 | 1.70) | (4.17 | 4 | 0.50) | (4.00 | 4 | 0.07) | (4.00 | 4 | 0.01) | (4.00 | 4 | 0.00) | U-NEWMA | 0.1 | 0.5958 | (200.09 | 139 | 196.95) | (43.21 | 32 | 37.14) | (10.51 | 9 | 5.99) | (5.64 | 5 | 2.45) | (3.90 | 4 | 1.44) | (2.75 | 3 | 0.88) | (1.94 | 2 | 0.57) | (1.58 | 2 | 0.51) | (1.13 | 1 | 0.34) | U-NEWMA | 0.2 | 0.9854 | (199.34 | 139 | 197.69) | (54.50 | 39 | 51.08) | (11.74 | 10 | 8.34) | (5.58 | 5 | 2.96) | (3.63 | 3 | 1.58) | (2.47 | 2 | 0.89) | (1.72 | 2 | 0.57) | (1.36 | 1 | 0.48) | (1.04 | 1 | 0.18) | U-NEWMA | 0.3 | 1.3314 | (200.22 | 140 | 198.80) | (66.24 | 47 | 63.94) | (14.12 | 11 | 11.51) | (5.98 | 5 | 3.76) | (3.66 | 3 | 1.83) | (2.38 | 2 | 0.96) | (1.61 | 2 | 0.57) | (1.26 | 1 | 0.44) | (1.01 | 1 | 0.12) | U-NEWMA | 0.5 | 1.9866 | (199.84 | 139 | 199.15) | (84.97 | 59 | 83.88) | (21.03 | 15 | 19.47) | (7.94 | 6 | 6.34) | (4.25 | 4 | 2.82) | (2.42 | 2 | 1.24) | (1.50 | 1 | 0.60) | (1.16 | 1 | 0.37) | (1.00 | 1 | 0.07) | U-NEWMA | 1 | 3.7043 | (199.48 | 138 | 198.99) | (112.28 | 78 | 111.99) | (40.68 | 28 | 39.97) | (17.30 | 12 | 16.79) | (8.44 | 6 | 7.86) | (3.70 | 3 | 3.17) | (1.61 | 1 | 1.00) | (1.13 | 1 | 0.39) | (1.00 | 1 | 0.04) | 9 | RR2,3-t | — | 1.8186 | (200.00 | 139 | 198.14) | (75.03 | 53 | 73.25) | (16.67 | 12 | 15.05) | (6.26 | 5 | 4.74) | (3.48 | 3 | 1.97) | (3.68 | 3 | 0.67) | (2.32 | 2 | 0.12) | (2.01 | 2 | 0.01) | (2.00 | 2 | 0.00) | RR3,4-t | — | 1.2011 | (200.00 | 139 | 197.17) | (65.11 | 46 | 62.44) | (13.70 | 10 | 11.29) | (5.82 | 4 | 3.48) | (3.85 | 3 | 1.39) | (3.13 | 3 | 0.40) | (3.00 | 3 | 0.05) | (3.00 | 3 | 0.00) | (3.00 | 3 | 0.00) | RR4,5-t | — | 0.8298 | (200.00 | 140 | 196.29) | (60.33 | 43 | 56.86) | (12.91 | 10 | 9.76) | (6.15 | 5 | 2.97) | (4.57 | 4 | 1.12) | (4.07 | 4 | 0.28) | (4.00 | 4 | 0.02) | (4.00 | 4 | 0.00) | (4.00 | 4 | 0.00) | U-NEWMA | 0.1 | 0.5614 | (200.00 | 140 | 195.72) | (35.53 | 27 | 29.59) | (8.61 | 8 | 4.53) | (4.74 | 4 | 1.88) | (3.33 | 3 | 1.12) | (2.38 | 3 | 0.76) | (1.73 | 2 | 0.50) | (1.73 | 2 | 0.50) | (1.02 | 1 | 0.15) | U-NEWMA | 0.2 | 0.9227 | (201.93 | 141 | 199.81) | (44.74 | 32 | 40.96) | (9.12 | 8 | 5.92) | (4.50 | 4 | 2.16) | (3.01 | 3 | 1.18) | (2.11 | 2 | 0.70) | (1.73 | 2 | 0.50) | (1.73 | 2 | 0.50) | (1.00 | 1 | 0.02) | U-NEWMA | 0.3 | 1.2367 | (200.65 | 140 | 199.17) | (54.12 | 38 | 51.22) | (10.42 | 8 | 7.82) | (4.60 | 4 | 2.57) | (2.93 | 2 | 1.31) | (1.98 | 2 | 0.73) | (1.36 | 1 | 0.49) | (1.36 | 1 | 0.49) | (1.00 | 1 | 1.01) | U-NEWMA | 0.5 | 1.8214 | (200.51 | 139 | 199.81) | (70.77 | 50 | 69.31) | (14.61 | 11 | 12.98) | (5.50 | 4 | 3.96) | (3.08 | 3 | 1.77) | (1.89 | 2 | 0.84) | (1.24 | 1 | 0.44) | (1.24 | 1 | 0.44) | (1.00 | 1 | 0.00) | U-NEWMA | 1 | 3.3526 | (198.40 | 138 | 197.83) | (100.79 | 70 | 100.13) | (30.40 | 21 | 29.85) | (11.56 | 8 | 11.04) | (5.31 | 4 | 4.77) | (2.33 | 2 | 1.77) | (1.20 | 1 | 0.49) | (1.20 | 1 | 0.49) | (2.00 | 2 | 0.00) | 11 | RR2,3-t | — | 1.7739 | (200.00 | 139 | 198.14) | (67.18 | 47 | 65.41) | (13.39 | 10 | 11.80) | (5.03 | 4 | 3.52) | (2.95 | 2 | 1.40) | (2.16 | 3 | 0.44) | (2.00 | 2 | 0.05) | (2.00 | 2 | 0.05) | (3.00 | 3 | 0.00) | RR3,4-t | — | 1.1833 | (200.00 | 139 | 197.17) | (58.16 | 41 | 55.50) | (11.33 | 9 | 8.95) | (4.98 | 4 | 2.63) | (3.52 | 3 | 0.99) | (3.06 | 4 | 0.25) | (3.00 | 3 | 0.02) | (3.00 | 3 | 0.00) | (4.00 | 4 | 0.00) | RR4,5-t | — | 0.8211 | (200.00 | 140 | 196.29) | (53.90 | 38 | 50.45) | (10.93 | 8 | 7.80) | (5.49 | 5 | 2.25) | (4.34 | 4 | 0.78) | (4.03 | 2 | 0.17) | (4.00 | 4 | 0.01) | (4.00 | 4 | 0.00) | (1.00 | 1 | 0.04) | U-NEWMA | 0.1 | 0.5430 | (199.45 | 140 | 195.98) | (30.77 | 24 | 24.80) | (7.52 | 7 | 3.71) | (4.19 | 4 | 1.56) | (2.97 | 3 | 0.94) | (2.15 | 2 | 0.60) | (1.58 | 2 | 0.50) | (1.20 | 1 | 0.40) | (1.00 | 1 | 0.00) | U-NEWMA | 0.2 | 0.8880 | (200.19 | 139 | 197.80) | (37.86 | 27 | 34.08) | (7.62 | 7 | 4.61) | (3.87 | 4 | 1.70) | (2.65 | 3 | 0.96) | (1.89 | 2 | 0.60) | (1.32 | 1 | 0.47) | (1.05 | 1 | 0.22) | (1.00 | 1 | 0.00) | U-NEWMA | 0.3 | 1.1838 | (199.62 | 139 | 197.84) | (45.53 | 32 | 43.01) | (8.33 | 7 | 5.85) | (3.85 | 3 | 1.96) | (2.52 | 2 | 1.03) | (1.74 | 2 | 0.62) | (1.20 | 1 | 0.40) | (1.02 | 1 | 0.14) | (1.00 | 1 | 0.00) | U-NEWMA | 0.5 | 1.7343 | (200.63 | 139 | 200.26) | (61.15 | 43 | 59.69) | (11.14 | 8 | 9.43) | (4.31 | 4 | 2.84) | (2.52 | 2 | 1.31) | (1.61 | 2 | 0.66) | (1.11 | 1 | 0.31) | (1.01 | 1 | 0.07) | (1.00 | 1 | 0.00) | U-NEWMA | 1 | 3.1667 | (199.08 | 139 | 197.97) | (91.00 | 63 | 90.52) | (24.05 | 17 | 23.66) | (8.34 | 6 | 7.81) | (3.76 | 3 | 3.22) | (1.73 | 1 | 1.12) | (1.07 | 1 | 0.40) | (1.00 | 1 | 0.05) | (1.00 | 1 | 0.00) |
|
|